I've never blown up an LED, but I have blown up other semiconductors.
The most memorable occasion was when I was working with some motor control hardware. The main power supply was a three phase, 240V, 40A per leg wall switch, which was rectified to about 300V DC with a some hefty diodes and a capacitor bank.
The circuit had previously been tested with 36V DC, and we were ramping up to full power.
The problem was a small design error on the 'logic' side of the system. There were diodes which were used as part of a 'charge pump' circuit to provide 12V _above_ the floating output of a transistor switching circuit, for gate drive. Basically a small 12V power supply was being used along with some diodes and a capacitor to supply a local 12V which might be referenced to the full 300V output of the main power supply. The problem was that I brain farted and selected diodes based upon the 12V supply, rather than the 300V supply.
When we applied full power, the diodes immediately started conducting, and connected the 300V main supply to the 12V supply. As soon as this happened, all hell broke loose.
Wires ignited. Resistors ignited. All of the ICs on the board went off like firecrackers, _loud_ firecrackers. Magic smoke poured out of my computer (I'd been really cowboy, and used the PC power supply as the 12V supply for the circuit...never again.) The 6 gauge wires which were laying on the floor between the wall switch and the apparatus literally jumped several inches because of the current flow.
The stench of burned resin and silicon hovered in the air for hours. All of the ICs had little craters in the center where the silicon dice had rapidly self dissembled. My boss was a touch disturbed, but luckily the power switch was on the other side of the room, and no-one was hurt.
We've also had a fully charged capacitor bank fail. Energy storage at failure was probably about 10,000WS, possibly higher. Apparently burning aluminium shot out of the enclosure, but for the most part the damage was properly contained. No other components failed during this accident, because we've learned lots about properly isolating failures.
-Jon